Problem: The value of $\sqrt{21}$ lies between which two consecutive integers ? Integers that appear in order when counting, for example 2 and 3.
Answer: Consider the perfect squares near $21$ . [ What are perfect squares? Perfect squares are integers which can be obtained by squaring an integer. The first 13 perfect squares are: $ 1,4,9,16,25,36,49,64,81,100,121,144,169$ $16$ is the nearest perfect square less than $21$ $25$ is the nearest perfect square more than $21$ So, we know $16 < 21 < 25$ So, $\sqrt{16} < \sqrt{21} < \sqrt{25}$ So $\sqrt{21}$ is between $4$ and $5$.